A drone's altitude above sea level during a test flight is modeled by a quadratic function $A(t)$, where $A(t)$ is the altitude in feet and $t$ is the time in minutes after takeoff. The drone is at an altitude of $500$ feet after $2$ minutes and again after $8$ minutes. Its maximum altitude during this flight was $900$ feet. How many minutes after takeoff did the drone return to sea level?